Online modeling with tunable RBF network

In this paper, we propose a novel online modeling algorithm for nonlinear and nonstationary systems using a radial basis function (RBF) neural network with a fixed number of hidden nodes. Each of the RBF basis functions has a tunable center vector and an adjustable diagonal covariance matrix. A multi-innovation recursive least square (MRLS) algorithm is applied to update the weights of RBF online, while the modeling performance is monitored. When the modeling residual of the RBF network becomes large in spite of the weight adaptation, a node identified as insignificant is replaced with a new node, for which the tunable center vector and diagonal covariance matrix are optimized using the quantum particle swarm optimization (QPSO) algorithm. The major contribution is to combine the MRLS weight adaptation and QPSO node structure optimization in an innovative way so that it can track well the local characteristic in the nonstationary system with a very sparse model. Simulation results show that the proposed algorithm has significantly better performance than existing approaches.

Synergistic effects of mixing cocksfoot and sainfoin on in vitro rumen fermentation: role of condensed tannins

Some bioactive secondary metabolites in forage legumes can cause digestive interactions, so that the rumen fermentation pattern of a mixture of forages can differ from the average values of its components. The objective of this study was to investigate the potential role of condensed tannins (CT) on the synergistic effects between one grass species, cocksfoot, and one CT-containing legume species, sainfoin, on in vitro rumen fermentation characteristics. Cocksfoot and sainfoin in different proportions (in g/kg, 1000:0, 750:250, 500:500, 250:750 and 0:1000) were incubated under anaerobic conditions in culture bottles containing buffered rumen fluid from sheep. Incubations were carried out using artificial saliva with and without polyethylene glycol (PEG), which binds and thus inactivates CT. Rumen fermentation parameters describing the degradation and the fate of the energetic and nitrogenous substrates were measured at 3.5 and 24 h. At the early fermentation stage, when the sainfoin level increased from 0 to 1000 g/kg, the ammonia concentration in the medium quadratically decreased from 3.20 to 0.53 mmol/l in absence of PEG (P<0.01) but not in its presence. This result demonstrates that sainfoin CT decreased the rumen degradation of the proteins in the whole mixture, including the proteins in cocksfoot, rather than just the proteins in sainfoin. Interestingly, the total gas and methane productions were lower in mixtures incubated in absence of PEG than in presence of PEG (P<0.001) while no significant PEG effect was observed on digestibility. At the late fermentation stage, a positive quadratic effect on dry matter digestibility was detected without PEG (P<0.05), indicating a synergistic action of cocksfoot plus sainfoin on plant substrate degradation due to CT. The presence of PEG increased gas production (P<0.001) and NH3-N concentration in the medium (P<0.001). Our results suggest that CT could allow a better utilization of plant substrates in mixtures by the rumen ecosystem by improving the partitioning of degraded substrates toward lower gas losses, and decreasing the protein degradation.

Land-atmosphere energy exchange in Arctic tundra and boreal forest: available data and feedbacks to climate

This paper summarizes and analyses available data on the surface energy balance of Arctic tundra and boreal forest. The complex interactions between ecosystems and their surface energy balance are also examined, including climatically induced shifts in ecosystem type that might amplify or reduce the effects of potential climatic change. High latitudes are characterized by large annual changes in solar input. Albedo decreases strongly from winter, when the surface is snow-covered, to summer, especially in nonforested regions such as Arctic tundra and boreal wetlands. Evapotranspiration (QE) of high-latitude ecosystems is less than from a freely evaporating surface and decreases late in the season, when soil moisture declines, indicating stomatal control over QE, particularly in evergreen forests. Evergreen conifer forests have a canopy conductance half that of deciduous forests and consequently lower QE and higher sensible heat flux (QH). There is a broad overlap in energy partitioning between Arctic and boreal ecosystems, although Arctic ecosystems and light taiga generally have higher ground heat flux because there is less leaf and stem area to shade the ground surface, and the thermal gradient from the surface to permafrost is steeper. Permafrost creates a strong heat sink in summer that reduces surface temperature and therefore heat flux to the atmosphere. Loss of permafrost would therefore amplify climatic warming. If warming caused an increase in productivity and leaf area, or fire caused a shift from evergreen to deciduous forest, this would increase QE and reduce QH. Potential future shifts in vegetation would have varying climate feedbacks, with largest effects caused by shifts from boreal conifer to shrubland or deciduous forest (or vice versa) and from Arctic coastal to wet tundra. An increase of logging activity in the boreal forests appears to reduce QE by roughly 50% with little change in QH, while the ground heat flux is strongly enhanced.

Movement of newly assimilated 13C carbon in the grass Lolium perenne and its incorporation into rhizosphere microbial DNA

One of the key processes that drives rhizosphere microbial activity is the exudation of soluble organic carbon (C) by plant roots. We describe an experiment designed to determine the impact of defoliation on the partitioning and movement of C in grass (Lolium perenne L.), soil and grass-sterile sand microcosms, using a (13)CO(2) pulse-labelling method. The pulse-derived (13)C in the shoots declined over time, but that of the roots remained stable throughout the experiment. There were peaks in the atom% (13)C of rhizosphere CO(2) in the first few hours after labelling probably due to root respiration, and again at around 100 h. The second peak was only seen in the soil microcosms and not in those with sterilised sand as the growth medium, indicating possible microbial activity. Incorporation of the (13)C label into the microbial biomass increased at 100 h when incorporation into replicating cells, as indicated by the amounts of the label in the microbial DNA, started to increase. These results indicate that the rhizosphere environment is conducive to bacterial growth and replication. The results also show that defoliation had no impact on the pattern of movement of (13)C from plant roots into the microbial population in the rhizosphere.

Genetic structure and linkage disequilibrium in landrace populations of barley in Sardinia

Multilocus digenic linkage disequilibria (LD) and their population structure were investigated in eleven landrace populations of barley (Hordeum vulgare ssp. vulgare L.) in Sardinia, using 134 dominant simple-sequence amplified polymorphism markers. The analysis of molecular variance for these markers indicated that the populations were partially differentiated (F ST = 0.18), and clustered into three geographic areas. Consistent with this population pattern, STRUCTURE analysis allocated individuals from a bulk of all populations into four genetic groups, and these groups also showed geographic patterns. In agreement with other molecular studies in barley, the general level of LD was low (13 % of locus pairs, with P < 0.01) in the bulk of 337 lines, and decayed steeply with map distance between markers. The partitioning of multilocus associations into various components indicated that genetic drift and founder effects played a major role in determining the overall genetic makeup of the diversity in these landrace populations, but that epistatic homogenising or diversifying selection was also present. Notably, the variance of the disequilibrium component was relatively high, which implies caution in the pooling of barley lines for association studies. Finally, we compared the analyses of multilocus structure in barley landrace populations with parallel analyses in both composite crosses of barley on the one hand and in natural populations of wild barley on the other. Neither of these serves as suitable mimics of landraces in barley, which require their own study. Overall, the results suggest that these populations can be exploited for LD mapping if population structure is controlled.

Sparse probability density function estimation using the minimum integrated square error

We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of kernels and the estimation of mixing weights. The proposed approach is simple to implement and the associated computational cost is very low. Specifically, the complexity of our algorithm is in the order of the number of training data N, which is much lower than the order of N2 offered by the best existing sparse kernel density estimators. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to those of the classical Parzen window estimate and other existing sparse kernel density estimators.

Metabifurcation analysis of a mean field model of the cortex

Mean field models (MFMs) of cortical tissue incorporate salient, average features of neural masses in order to model activity at the population level, thereby linking microscopic physiology to macroscopic observations, e.g., with the electroencephalogram (EEG). One of the common aspects of MFM descriptions is the presence of a high-dimensional parameter space capturing neurobiological attributes deemed relevant to the brain dynamics of interest. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two archetypal categories or “families”. After investigating and characterizing them in depth, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli such as thalamic input, and distributions of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs significantly between families, we are able to show how metamorphoses between the families can be brought about by exogenous stimuli. We here unveil links between measurable physiological attributes of the brain and dynamical patterns that are not accessible by linear methods. They instead emerge when the nonlinear structure of parameter space is partitioned according to bifurcation responses. We call this general method “metabifurcation analysis”. The partitioning cannot be achieved by the investigation of only a small number of parameter sets and is instead the result of an automated bifurcation analysis of a representative sample of 73,454 physiologically admissible parameter sets. Our approach generalizes straightforwardly and is well suited to probing the dynamics of other models with large and complex parameter spaces.

Quantification of chemical and physical processes influencing ozone during long-range transport using a trajectory ensemble

During long-range transport, many distinct processes – including photochemistry, deposition, emissions and mixing – contribute to the transformation of air mass composition. Partitioning the effects of different processes can be useful when considering the sensitivity of chemical transformation to, for example, a changing environment or anthropogenic influence. However, transformation is not observed directly, since mixing ratios are measured, and models must be used to relate changes to processes. Here, four cases from the ITCT-Lagrangian 2004 experiment are studied. In each case, aircraft intercepted a distinct air mass several times during transport over the North Atlantic, providing a unique dataset and quantifying the net changes in composition from all processes. A new framework is presented to deconstruct the change in O3 mixing ratio (Δ O3) into its component processes, which were not measured directly, taking into account the uncertainty in measurements, initial air mass variability and its time evolution. The results show that the net chemical processing (Δ O3chem) over the whole simulation is greater than net physical processing (Δ O3phys) in all cases. This is in part explained by cancellation effects associated with mixing. In contrast, each case is in a regime of either net photochemical destruction (lower tropospheric transport) or production (an upper tropospheric biomass burning case). However, physical processes influence O3 indirectly through addition or removal of precursor gases, so that changes to physical parameters in a model can have a larger effect on Δ O3chem than Δ O3phys. Despite its smaller magnitude, the physical processing distinguishes the lower tropospheric export cases, since the net photochemical O3 change is −5 ppbv per day in all three cases. Processing is quantified using a Lagrangian photochemical model with a novel method for simulating mixing through an ensemble of trajectories and a background profile that evolves with them. The model is able to simulate the magnitude and variability of the observations (of O3, CO, NOy and some hydrocarbons) and is consistent with the time-average OH following air-masses inferred from hydrocarbon measurements alone (by Arnold et al., 2007). Therefore, it is a useful new method to simulate air mass evolution and variability, and its sensitivity to process parameters.

On the 'downward control' of extratropical diabatic circulations by eddy-induced mean zonal forces

The situation considered is that of a zonally symmetric model of the middle atmosphere subject to a given quasi-steady zonal force F̄, conceived to be the result of irreversible angular momentum transfer due to the upward propagation and breaking of Rossby and gravity waves together with any other dissipative eddy effects that may be relevant. The model's diabatic heating is assumed to have the qualitative character of a relaxation toward some radiatively determined temperature field. To the extent that the force F̄ may be regarded as given, and the extratropical angular momentum distribution is realistic, the extratropical diabatic mass flow across a given isentropic surface may be regarded as controlled exclusively by the F̄ distribution above that surface (implying control by the eddy dissipation above that surface and not, for instance, by the frequency of tropopause folding below). This “downward control” principle expresses a critical part of the dynamical chain of cause and effect governing the average rate at which photochemical products like ozone become available for folding into, or otherwise descending into, the extratropical troposphere. The dynamical facts expressed by the principle are also relevant, for instance, to understanding the seasonal-mean rate of upwelling of water vapor to the summer mesopause, and the interhemispheric differences in stratospheric tracer transport. The robustness of the principle is examined when F̄ is time-dependent. For a global-scale, zonally symmetric diabatic circulation with a Brewer-Dobson-like horizontal structure given by the second zonally symmetric Hough mode, with Rossby height HR = 13 km in an isothermal atmosphere with density scale height H = 7 km, the vertical partitioning of the unsteady part of the mass circulation caused by fluctuations in F̄ confined to a shallow layer LF̄ is always at least 84% downward. It is 90% downward when the force fluctuates sinusoidally on twice the radiative relaxation timescale and 95% if five times slower. The time-dependent adjustment when F̄ is changed suddenly is elucidated, extending the work of Dickinson (1968), when the atmosphere is unbounded above and below. Above the forcing, the adjustment is characterized by decay of the meridional mass circulation cell at a rate proportional to the radiative relaxation rate τr−1 divided by {1 + (4H2/HR2)}. This decay is related to the boundedness of the angular momentum that can be taken up by the finite mass of air above LF̄ without causing an ever-increasing departure from thermal wind balance. Below the forcing, the meridional mass circulation cell penetrates downward at a speed τr−1 HR2/H. For the second Hough mode, the time for downward penetration through one density scale height is about 6 days if the radiative relaxation time is 20 days, the latter being representative of the lower stratosphere. At any given altitude, a steady state is approached. The effect of a rigid lower boundary on the time-dependent adjustment is also considered. If a frictional planetary boundary layer is present then a steady state is ultimately approached everywhere, with the mass circulation extending downward from LF̄ and closing via the boundary layer. Satellite observations of temperature and ozone are used in conjunction with a radiative transfer scheme to estimate the altitudes from which the lower stratospheric diabatic vertical velocity is controlled by the effective F̄ in the real atmosphere. The data appear to indicate that about 80% of the effective control is usually exerted from below 40 km but with significant exceptions up to 70 km (in the high latitude southern hemispheric winter). The implications for numerical modelling of chemical transport are noted.

Mobile-to-mobile MIMO transmit-receive diversity systems: analysis and performance in three-dimensional double-correlated channels

Mobile-to-mobile (M-to-M) communications are expected to play a crucial role in future wireless systems and networks. In this paper, we consider M-to-M multiple-input multiple-output (MIMO) maximal ratio combining system and assess its performance in spatially correlated channels. The analysis assumes double-correlated Rayleigh-and-Lognormal fading channels and is performed in terms of average symbol error probability, outage probability, and ergodic capacity. To obtain the receive and transmit spatial correlation functions needed for the performance analysis, we used a three-dimensional (3D) M-to-M MIMO channel model, which takes into account the effects of fast fading and shadowing. The expressions for the considered metrics are derived as a function of the average signal-to-noise ratio per receive antenna in closed-form and are further approximated using the recursive adaptive Simpson quadrature method. Numerical results are provided to show the effects of system parameters, such as distance between antenna elements, maximum elevation angle of scatterers, orientation angle of antenna array in the x–y plane, angle between the x–y plane and the antenna array orientation, and degree of scattering in the x–y plane, on the system performance. Copyright © 2011 John Wiley & Sons, Ltd.

Trade-offs and responsiveness of the single-layer urban canopy parametrization in WRF: an offline evaluation using the MOSCEM optimization algorithm and field observations

For an increasing number of applications, mesoscale modelling systems now aim to better represent urban areas. The complexity of processes resolved by urban parametrization schemes varies with the application. The concept of fitness-for-purpose is therefore critical for both the choice of parametrizations and the way in which the scheme should be evaluated. A systematic and objective model response analysis procedure (Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm) is used to assess the fitness of the single-layer urban canopy parametrization implemented in the Weather Research and Forecasting (WRF) model. The scheme is evaluated regarding its ability to simulate observed surface energy fluxes and the sensitivity to input parameters. Recent amendments are described, focussing on features which improve its applicability to numerical weather prediction, such as a reduced and physically more meaningful list of input parameters. The study shows a high sensitivity of the scheme to parameters characterizing roof properties in contrast to a low response to road-related ones. Problems in partitioning of energy between turbulent sensible and latent heat fluxes are also emphasized. Some initial guidelines to prioritize efforts to obtain urban land-cover class characteristics in WRF are provided. Copyright © 2010 Royal Meteorological Society and Crown Copyright.

A nonparametric ensemble transform method for Bayesian inference

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables. © 2013, Society for Industrial and Applied Mathematics

The role of horizontal resolution in simulating drivers of the global hydrological cycle

The role of atmospheric general circulation model (AGCM) horizontal resolution in representing the global energy budget and hydrological cycle is assessed, with the aim of improving the understanding of model uncertainties in simulating the hydrological cycle. We use two AGCMs from the UK Met Office Hadley Centre: HadGEM1-A at resolutions ranging from 270 to 60 km, and HadGEM3-A ranging from 135 to 25 km. The models exhibit a stable hydrological cycle, although too intense compared to reanalyses and observations. This over-intensity is explained by excess surface shortwave radiation, a common error in general circulation models (GCMs). This result is insensitive to resolution. However, as resolution is increased, precipitation decreases over the ocean and increases over the land. This is associated with an increase in atmospheric moisture transport from ocean to land, which changes the partitioning of moisture fluxes that contribute to precipitation over land from less local to more non-local moisture sources. The results start to converge at 60-km resolution, which underlines the excessive reliance of the mean hydrological cycle on physical parametrization (local unresolved processes) versus model dynamics (large-scale resolved processes) in coarser HadGEM1 and HadGEM3 GCMs. This finding may be valid for other GCMs, showing the necessity to analyze other chains of GCMs that may become available in the future with such a range of horizontal resolutions. Our finding supports the hypothesis that heterogeneity in model parametrization is one of the underlying causes of model disagreement in the Coupled Model Intercomparison Project (CMIP) exercises.

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data.

A fast algorithm for sparse probability density function construction

A new sparse kernel density estimator is introduced. Our main contribution is to develop a recursive algorithm for the selection of significant kernels one at time using the minimum integrated square error (MISE) criterion for both kernel selection. The proposed approach is simple to implement and the associated computational cost is very low. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.